Flutter-type dynamic instability induced by friction is a highly nonlinear phenomenon and computationally expensive to model through transient analysis. An efcient way to make inference of such instabilities in a dynamical system is through analyzing the frst-order efect of a perturbation at one of its equilibrium with eigenvalue analysis. Te contact characteristics of such dynamical systems are typically modelled through the normal compliance approach with inference from experiments. In this case, the dynamical response of the system is implied to be sensitive to the contact stifness modelled through the normal compliance approach. Typically, with the normal compliance approach, the continuum of the contact interface is approximated through a set of nonlinear springs which can be interpreted as a collocation method. Such approximations or the numerical implication of contact formulations in general for such problems is not largely studied. We focus on a variational formulation-based contact formulation without domain decomposition which is computationally efcient with small sacrifce in accuracy, where we imply that the dynamical response can be robustly modelled with the given accuracy. Further, we expose the inadequacy of the collocation method for such problems, where the dynamical system is observed to be sensitive to the extent of inaccuracy as a result of collocation for low values of contact stifness. Te inferences numerically imply the characteristics of the dynamical system for variation in contact stifness.